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Ariel Hernandez (Power Point) Michellene Saegh ( Problem Solving)PowerPoint Presentation

Ariel Hernandez (Power Point) Michellene Saegh ( Problem Solving)

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Ariel Hernandez (Power Point)

MichelleneSaegh(Problem Solving)

and Raynelle Salters (Graphing)

R(x) = (X4) / (X2 - 9)

Step 1: < FACTOR >

R(x) = (X4) / (X2 - 9)

R(x) = (X4) / (x-3)(x+3)

FIND THE DOMAIN

R(x) = (X4) / (x-3)(x+3)

You have (x-3)(x+3) in the

Denominator

So set them equal to Zero

x-3 = 0 and x+ 3= 0

x ≠ 3 x ≠ -3

The Domain is all real numbers except:

x = 3 and x = -3

Find the Vertical Asymptotes

Take the Denominator of the Function

R(x) = (X4) / (X2 - 9)

and set it equal to zero

X2 – 9 = 0

X2 = 9

√x2 = √9

X = 3 and -3

So since X = 3 and X= -3 then that means the function R(x) = (X4) / (X2 - 9)

Has two vertical asymptotes

One at X = -3 and the other at X = 3

Step 4: Finding the Horizontal Asymptotes

To find the Horizontal Asymptotes of the Function

R(x) = (X4) / (X2 - 9)

Compare the Degrees of the numerator and the denominator

In this case

The Numerator has aX4with a degree of 4

The Denominator has X2 with a degree of 2

Therefore : The N(4) > D(2)

So according the Rule about Horizontal Asymptotes

In which the degree of the numerator is n

and degree of the denominator is m.

If n > m + 1

That tells you that the Graph of R has neither a horizontal behavior nor an oblique asymptote.

So NO Horizontal Asymptote for R(x) = (X4) / (X2 - 9)

Finding the x and y intercepts of R(x) = (X4) / (X2 - 9)

For the x-intercept

Set R(x) = (X4) / (X2 - 9) = 0 and solve

(X4) / (X2 - 9) = 0

(X4) = 0

4√(X4= 4√0

X= 0

Therefore the x-intercept for R(x) = (X4) / (X2 - 9)

Is (0, 0)

For the y-intercept

Plug in Zero in place of X R(x) = (X4) / (X2 - 9) to find the x coordinate

R(x) = (04) / (02 - 9)

y = (0) / (- 9)

y = 0

Therefore the y-interceptfor R(x) = (X4) / (X2 - 9)

Is (0,0)

R(x) = (X4) / (X2 - 9)

X-intercept (0,0) and Y-intercept (0,0)

Graph of R(x) = (X4) / (X2 - 9) Zoomed in.

Graph of R(x) = (X4) / (X2 - 9)

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